基于欧进萍谱的广义Maxwell耗能结构随机响应简明解法

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摘要针对设置广义Maxwell阻尼器多自由度耗能结构在欧进萍谱激励下响应分析较复杂的问题，提出了一种求解系统响应简洁的解析解法。首先，将广义Maxwell阻尼器本构方程、原结构运动方程与欧进萍谱滤波方程联立，重构结构运动方程；然后，采用复模态法将其解耦，得到结构位移及结构速度、层间位移及层间速度、阻尼器受力及其变化率等响应基于白噪声激励的统一杜哈梅积分表达式；最后，根据功率谱密度函数与其协方差函数的Wiener-Khinchin关系，获得了耗能结构及阻尼器响应谱矩的简明解析解。算例通过与虚拟激励法进行对比，表明了该方法的正确性，同时也具有更高计算效率的优点。

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	刘美华
	邹万杰
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	李创第

关键词 ：广义Maxwell阻尼器, 欧进萍谱, 地震响应, 谱矩, 简明解析解

Abstract：To address the complexity of the seismic responses analysis of multiple-storey structure with generalized Maxwell dampers under Ou Jinping spectrum excitation, a concise analytic solution was proposed. Firstly, the structural equation of motion was reconstructed by associating the constitutive equations of the generalized Maxwell dampers, the original structural equation and the Ou Jinping spectrum filter equations. Then, decoupled the system was decoupled by using the complex mode method, the uniform Duhamel integral expressions based on white noise excitation for the dynamic responses of absolute displacement and absolute velocity, inter-storey displacement and inter-storey velocity, damping force and damping force change rate were obtained. Finally, according to the Wiener-Khinchin relationship between the power spectrum density function and covariance function, the concise analytic solution of the the spectral moments for the structure and damper were obtained.After comparing with the pseudo excitation method,The examplethe result showesed the correctness of the proposed method by comparing with the pseudo excitation method, and which also had has the an advantage of higher computational efficiency.

Key words： generalized Maxwell damper Ou Jinping spectrum seismic response spectral moments concise analytic solution

收稿日期: 2021-05-19 出版日期: 2022-02-28

引用本文:

刘美华，邹万杰，葛新广，李创第. 基于欧进萍谱的广义Maxwell耗能结构随机响应简明解法[J]. 振动与冲击, 2022, 41(4): 124-133.
LIU Meihua, ZOU Wanjie, GE Xinguang, LI Chuangdi. A concise analytic solution to seismic response of structure with generalized Maxwell dampers under Ou Jinping spectrum excitation. JOURNAL OF VIBRATION AND SHOCK, 2022, 41(4): 124-133.

链接本文:

http://jvs.sjtu.edu.cn/CN/ 或 http://jvs.sjtu.edu.cn/CN/Y2022/V41/I4/124

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